1. Field of the Invention
The present invention generally relates to a technique for filtering signals, and more particularly to a technique for extracting a desired component from signals transmitted by an artifical satellite and smeared by noise.
Furthermore, the present invention relates to a signal parameter estimation, and more particularly to a technique for estimating signal parameters by processing the signal composed of two or more signals which are mutually coherent and the frequencies of which are rational to each other, and that rapidly change its parameters such as accelerated Doppler frequency.
The present invention relates to a technique for determining the receiver position or for estimating orbital parameters of an artifical heavenly body by recovering phase signal from a received signal and analysing them, and more particularly to a technique for determining the position on or near by the surface of the Earth by receiving signals transmitted from the NAVSTAR/Global Positioning System (GPS)(which is) described in detail in a publication "SYSTEM SPECIFICATION FOR THE NAVSTAR GLOBAL POSITIONING SYSTEM, SS-GPS-300B, Mar. 3, 1980".
Furthermore, the present invention relates to a technique for determining the baseline sector between a pair of receiver points or the baseline network consist of several receiver points on or near by the surface of the Earth by analysing the signals received by the receivers respectively.
The present invention relates to an apparatus for performing the absolute positioning or the relative positioning by receiving and analysing the signals transmitted from the GPS satellite and more particularly PLL (Phase Locked Loop) an apparatus for reproducing the original signal as faithful as possible.
2. Description of the Related Art
The theoretical background of this patent will be described herein with reference to a geodetic positioning system utilizing a GPS. The fact described below is universal and can be easily applied to similar geodetic positioning systems, as a matter of course. Time series signal s(t) is generally given by: EQU s(t)=A(t)exp{j.PHI.(t)} (1)
where A(t) is the amplitude of the signal, j is .sqroot.-1 and .PHI.(t) is the phase of the signal.
If two signals s.sub.1 (t) and s.sub.2 (t) are given by the following equations: EQU s.sub.1 (t)=A.sub.1 (t)exp{j.PHI..sub.1 (t)} (2-1) EQU s.sub.2 (t)=A.sub.2 (t)exp{j.PHI..sub.2 (t)} (2-2)
when these signals are coherent to each other, the two phase components .PHI..sub.1 (t) and .PHI..sub.2 (t) have a relation: EQU .PHI..sub.2 (t)=k.PHI..sub.1 (t)+n(t)+.PHI..sub.0 ( 3)
Where k is a constant, .PHI..sub.0 is the constant phase shift, and n(t) is a mean value of which represents the Erogodic random (noise) with zero mean value. In other words, when the two signals are coherent to each other, a phase ratio of the two signals must be fixed, and a phase difference between the two signals must be resented by the Ergodic stochastic process. A signal generated from a space vehicle is often a composite signal of some signals having a coherent phase relationship. In particular, this fact is conspicuous for a signal generated from a GPS satellite.
The signal format of a GPS satellite can be given by the following equation, as described in Sections 6 and 7 of the article entitled "Guide to GPS positioning, Prepared under the Leadership of David Wells, Canadian GPS Associates, 1986": ##EQU1## where Ac is the modulation level of a C/A (Coarse/Acquisition) code, Ap is the modulation level of a P (Precision) code, C(t) is the binary C/A-code modulation signal having a chip rate of 1.023 Mbps, P(t) is the binary P-code modulation signal having a chip rate of 10.23 Mbps, D(t) is the binary data modulation signal having a baud rate of 50 bps, f.sub.1 is the carrier frequency of L.sub.1, f.sub.2 is the carrier frequency of L.sub.2, .PHI.c is the initial phase of the C/A-code modulation signal, and .PHI..sub.p is the initial phase of the P-code modulation signal.
The characteristic feature of a signal from a GPS satellite is remarkably different from that of a conventional digital communication system in that the frequencies of all the modulation signal clocks and all the carriers are coherent to each other, and have integral ratio (rational) relationships. More specifically, if a fundamental frequency=f.sub.0, the relationships among the frequencies are given by: EQU f.sub.C/A =f.sub.0 /10 (5-1) EQU f.sub.p =f.sub.0 ( 5-2) EQU f.sub.L1 =154f.sub.0 ( 5-3) EQU f.sub.L2 =120f.sub.0 ( 5-4)
where f.sub.0 is the fundamental frequency=10.23 MHz, f.sub.C/A is the chip rate of the C/A code, f.sub.p is the chip rate of the P code, f.sub.L1 is the L.sub.1 carrier frequency, and f.sub.L2 is the L.sub.2 carrier frequency.
The relationships among the phase signals obtained by reproducing the clocks of the C/A and P codes and the phase signals of the two carriers are thus derived as follows: EQU .PHI..sub.p (t)=10.PHI..sub.C/A (t) (6-1) EQU .PHI..sub.L1 (t)=154.PHI..sub.p (t) (6-2) EQU .PHI..sub.L2 (t)=120.PHI..sub.p (t) (6-3)
where .PHI..sub.C/A (t) is the clock phase signal of the C/A code, .PHI..sub.p (t) is the clock phase signal of the P code, .PHI.L.sub.1 (t) is the phase signal of the L.sub.1 carrier, and .PHI.L.sub.2 (t) is the phase signal of the L.sub.2 carrier.
Time function r(t) of a range between an artificial celestial body and a receiver station can be given by the following equation using phase signal .PHI.r(t) obtained by reproducing the signal generated from the artificial celestial body: EQU r(t)=-.lambda..multidot..PHI.r(t)/(2.pi.)+B.multidot.c (7)
where .lambda. is the wavelength of the phase signal, B is the time bias between the time system of the space vehicle and the time system of the receiver station, and c is the velocity of light.
Time function .rho.(t) obtained by omitting the second term of the right-hand side of the equation (.eta.) is called a pseudo range since it is biassing as B.C. as against to the true range .gamma.(t). The pseudo range function .rho.(t) is presented by the flowing equation. EQU .rho.(t)=-.lambda..multidot..PHI.r(t)/(2.pi.) (8)
(Therefore) The positioning or ranging system utilizing GPS signals is required to recover (restore) the phase signal .PHI..gamma.(t) as faithful as possible. EQU .rho.(t)=-.lambda..multidot..PHI.r(t)/(2.pi.) (8)
In this manner, one of positioning techniques in a GPS positioning system is a technique of performing positioning by reproducing the above-mentioned phase signals as faithful as possible and obtaining a pseudo range based on the reproduced signal. However, in the conventional technique, the phase signals are independently reproduced without utilizing frequency relationships given by equations (5-1) to (5-4) and phase relationships given by equations (6-1) to (6-3).
In the conventional technique, however, the frequency relationships given by equations (5-1) to (5-4) and the phase relationships given by equations (6-1) to (6-3) are not utilized, and the PLL performance cannot be fully exhibited. Since a GPS satellite is a revolving satellite which goes around the earth once in about 12 hours, the receiving signal suffers from the Doppler effect due to the relative movement between the rotation of the earth and the movement of the satellite. The frequency shift and accelerated frequency shift of the receiving signal as a result of the Doppler effect are a maximum of about 3.times.10.sup.-6 Hz/Hz and about 6.5.times.10.sup.-10 Hz/Hz/sec, respectively. Thus, it is not easy to design a PLL which can be locked with such signals and can stably operate. In the PLL according to the conventional technique, the following problems are posed:
(1) Natural angular frequency .omega..sub.n of the PLL cannot be decreased much; and
(2) The sampling frequency of the signal must be selected to be twice or more the maximum Doppler frequency shift to prevent an aliasing distortion problem.
Natural angular frequency .omega..sub.n of the PLL must be as low as possible in order to enhance the noise reduction effect of the PLL. Therefore, in the conventional technique, the noise reduction effect of the PLL is limited by the problem (1). Since the problem (2) undesirably determines the lower limit of the sampling frequency, a data volume required for signal processing is increased, and then much time is required for processing. In the PLL according to the conventional technique, due to the presence of the acceleration Doppler frequency shift, the following problem is also posed:
(1) A doubly integrated 3rd order or more higher order PLL must be selected as the PLL.
The problem (1) is posed because a PLL of the 3rd order must be employed so as to be phase-locked with a signal including the acceleration Doppler frequency shift (also called a frequency ramp) and not to cause a phase shift error in a steady state. However, a PLL of the 3rd order or higher is difficult to design. If possible, such a PLL generally cannot be stably operated.
More specifically, in the conventional technique, in order to reproduce a signal from an artificial celestial body, the receiving signal is often directly filtered and reproduced by a PLL.
Since receiving signal .PHI.r(t) is influenced by the relative movement between the artificial celestial body and the receiver station, it becomes a signal which changes rapidly. For example, in the case of the signal from a GPS satellite which goes around the earth once in about 12 hours, as described above, the frequency shift and acceleration frequency shift of the receiving signal caused by the Doppler effect are respectively a maximum of about 3.times.10.sup.-6 Hz/Hz and about 6.5.times.10.sup.-10 Hz/Hz/sec.
In general, a signal from a space vehicle is often a signal of very low C/N.sub.0 ratio (a ratio of signal power to a power density of noise). The technique using a PLL as described above as a method of reproducing such a signal poses some problems.
One of the problems is "lock-in" problem. The lock-in characteristic of a PLL is mainly determined by the C/N.sub.0 ratio of an input signal and the natural angular frequency of the PLL. If the input signal is a signal free from a change in frequency, i.e., the signal is a composite signal of a line spectrum signal and noise, then it always possible to design a PLL that can be locked to the line spectrum signal even if the C/N.sub.0 ratio of the composite signal is very low by reducing the natural angular frequency of the PLL as needed (required). However, if the input signals is a composite signal of a signal having a large change in frequency and noise, the natural angular frequency of the PLL must be large enough in accordance with the magnitude of the change in frequency of the signal. In this case, the PLL cannot always be locked in depending on the C/N.sub.0 ratio of the input signal. When the PLL is designed to have a high natural angular frequency, the S/N ratio of the processed signal of the PLL is degraded, and under some conditions, locking cannot be kept. If a point of compromise against these conflicting requirements cannot be found out, under some conditions of the input signal, a PLL which is locked in that signal cannot be designed. Meanwhile, if the high natural angular frequency of a PLL is set, the noise reduction effect is reduced. Thus, even if a PLL which can be locked in the above-mentioned signal can be designed, it is not preferable in view of the noise reduction effect of the PLL.
The second problem is associated with the order of a PLL (the highest order of the PLL response function represented by the Laplace transform). When a popular 2rd-order type is used as the order of the PLL, the response of the PLL has a phase error according to the magnitude of a change in frequency of the input signal, as is theoretically known. For this reason, when a signal which changes largely is required to be reproduced with high accuracy, a PLL of the 3rd order or higher must be employed.
However, a PLL of the 3rd order is difficult to design. If possible, a PLL of this type generally cannot be stably operated.
As a solution to the above-mentioned problems, a residual signal processing technique described below is known.
The residual signal processing is a technique for processing a residual between the input signal and a predicted value of the input signal instead of directly processing the input signal. Thus, the input signal to a PLL can be converted to a signal approximated to a DC one, which has a small change in frequency. Thus, the above-mentioned problems can be largely eliminated.
However, in this technique, the predicted value of the input signal must be calculated along with time. In general, a predicted value of an input signal must be calculated based on an estimated orbital parameters of a space vehicle and estimated position data of a receiver station. Therefore, the following problems are posed:
(1) The presumed orbital parameters of the artificial celestial body and the presumed position of the receiver station must be acquired in advance.
(2) A relatively complicated calculation must be made, and real-time processing and hardware are difficult to realize.
In recent years, a signal processing system is constituted by a discrete system. In this case, a signal must be sampled and quantized to perform digital processing. In this description, since signal quantization can be assumed to be achieved with infinite precision, there is no technical problem.
A signal must be sampled at a sampling frequency twice or more an effective band width of a signal according to the sampling theorem. For example, when an L.sub.1 carrier signal is processed by a discrete system, since the maximum Doppler frequency of the L.sub.1 carrier signal becomes about .+-.4.5 kHz, sampling must be made using a sampling frequency of 9 kHz or higher. It is theoretically redundant to process the signal at a sampling frequency given (determined) by the sampling theory, if the power spectrum of the signal is concentrated around the principal component of the signal by prefiltering. However, in this case, the sampling frequency cannot be easily decreased, i.e., undersampling processing cannot be easily employed because of the problem of aliasing distortion.